To reasonably evaluate the thermal safety of explosive, the cook-off process for RDX-based polymer bonded explosive (PBX) cylinder was numerically simulated using self-written finite element software—dynamic response simulation package for energetic materials. The kinetic process of multi-step thermal decomposition reaction for explosive was realized. Change rule of the mass fraction of each components with temperature in the ignition area was explored. Results show that the primary thermal decomposition reaction at 400 K begins to accelerate. At 450 K, the secondary decomposition reaction occurs obviously. At 460 K, the third step reaction begins to accelerate, the final gas product gradually accumulates. When the mass fraction of final gas product is 0.006%, the ignition occurs. In addition, with the increase of heating rate, the ignition time of explosive is rapidly decayed and the temperature of the center is decreased.